Abstract:
A paradox is a real phenomenon, which contradicts ordinary insights and
human intuition. Paradoxes are milestones of science.
Two-phase bubbly fluids manifest a number of paradoxical properties. In
spite of the negligible amount of the gas (mass concentration $\sim $
10$^{-5})$ the thermo-physical properties of the gas in the bubbles exert a
significant influence on the shock and acoustic wave attenuation. At the
same time the variation in viscosity and other thermo-physical properties of
the liquid, which composes almost all of the bubbly liquid mass has little
influence on wave attenuation.
It is common for the bubbly liquid to damp the shock, but for some regimes
the shock waves can be strongly amplified by bubbly liquids. The basis for
this phenomenon is determined by a very specific property of the bubbly
liquid known as a local volume deformation inertia when the pressure depends
not only on the density, $\rho $, but on the acceleration of compression,
$\ddot{{\rho }}$.
The third paradox of bubbly liquid is connected with the bubble motion in a
vertical column with a bottom subjected to intensive vertical vibration
($\omega \sim $10 Hz). For specific regimes gas bubbles can be entrained
on the upper surface of liquid and move down forming a gas cushion on the
bottom of the column. This cushion may initiate additional vertical
oscillations with frequency, $\Omega $. Interaction of these two frequencies
may be resonant and initiate motion of the bubbles down and up. This
phenomena can be used for very effective mixing of two liquids which
normally are mixed poorly.
Many paradoxes are manifested in sonoluminescence and bubble fusion
experiments (Taleyarkhan, West, Cho, Lahey, Nigmatulin, Block, 2002, 2004,
2006). The last experiments showed that neutron emission and tritium
formation may occur in deutorated acetone under acoustic cavitation
conditions. Intensity of the fast neutron (2.5 MeV) emission and tritium
nucleus production is 10$^{4}$ - 10$^{6}$ s$^{-1}$. This suggests ultrahigh
compression of the matter produced inside the bubbles during their collapse.
Systematic research is being carried out on vapor bubble implosion in
intense acoustic fields in D-acetone (C$_{3}$DO$_{6})$ to provide the
observed effect theoretical confirmation and explanation. The dynamics of
the bubbles formed during maximum rarefaction in the liquid is numerically
studied on the basis of the models developed for a single bubble and bubble
clusters. It is assumed that during their growth the bubbles coagulate and
form a few bigger bubbles, which then collapse under the additional pressure
pulses produced in the liquid through the amplification of compression waves
within the cluster. A shock wave is shown to be formed inside the bubble
during the latter's rapid contraction. Focusing of this shock wave in the
bubble center initiates dissociation and ionization, results in violent
increases ($0.77\times 10^{5}$ times) in density (10$^{4}$ kgm$^{3})$,
pressure (10$^{10}$-10$^{11}$ bar) and temperature 10$^{8}$-10$^{9}$ K),
high enough to produce nuclear fusion reactions. The bubble looks like a
nano-hydrogen bomb. The diameter of the neutron emission zone is about 100
nm. The highest neutron emission is recorded at about 25 nm from the bubble
center. The number of neutrons emitted during the implosion of a single
bubble is $\sim $10 neutrons per implosion, and the number of tritium nuclei
is the same. It is found out that the intensity of bubble implosion and the
number of neutron emitted increase with variations in nucleation phase,
positive half-wave amplitude, and liquid.
Some important features of the process analyzed in our theoretical paper
(Nigmatulin et al, 2005) were:
The cold liquid effect, where relatively small variations of the liquid pool temperature strongly influence the acceleration of the liquid and intensity of the thermonuclear fusion reaction.
The bubble cluster effect, where multi-bubble cluster dynamics produce an amplification of compression compared with the incident pressure of acoustical field
Non-dissociation of the liquid, where, in spite the high pressures and temperature experienced on the interface (10$^{5}$ – 10$^{6}$ bar, 2500 K) the liquid has insufficient time for dissociation during 10 ns. That is why the liquid is much less compressible than implied by the equilibrium adiabat which corresponds to more than a microsecond of compression. Thus only the extrapolation of first part of D-U shock adiabat should be used for the estimation of compressibility of the liquid.
“Cold” electrons. During the extremely short time of the compression (10$^{-13}$ – 10$^{-12}$ s) the electrons have no time to be heated by ions. Thus the heat capacity of the gas/vapor is $\sim $ 2,000 J/kg instead of the equilibrium heat capacity of fully ionized plasma, $\sim $ 8,000 J/kg. This allows the temperature of ions to be four times higher than for an equilibrium plasma which results in conditions suitable for thermonuclear fusion. Moreover the “cold” electrons do not produce intensive energy losses by photon emissions.
Intensive collapse of the bubble is a multi-scale phenomena with the final sharpening. During the different stages the different physical phenomena, spatial and time scales dominate the process. These physical processes are: heat transfer, evaporation, condensation, transition from two phase to supercritical fluid, transition from a non-compressible liquid and a homobaric pressure distribution in the vapor (this stage takes almost all the time of the process (41.5 $\mu $s from 42 $\mu $s) to high compression of the liquid and to shock wave phenomena in gas (0.5 $\mu $s), dissociation, ionization and finally to nuclear fusion). The spatial scales are the following: acoustical field scale is $\sim $ 10$^{-2}$ m, cluster scale is $\sim $10$^{-3}$ m, bubble scale is $\sim $ 10$^{-5}$ – 10$^{-4}$ m, dissociation and ionization cores scale is $\sim $ 10$^{-7}$ - 10$^{-6}$ m, thermonuclear core scale is 10$^{-8}$ – 10$^{-7}$ m. The time scales are the following: evaporation and condensation scale is $\sim $ 10$^{-5}$ s, compression wave scale is $\sim $10$^{-6}$ s, dissociation and ionization scale is $\sim $10$^{-9}$ s, and thermonuclear time scale is 10$^{-13}$ s. The numerical code needs to vary the equations to accommodate the different physical phenomena and different sizes of the grid and different time steps form $\Delta t =$10$^{-7}$ s to 10$^{-14}$ s. To clarify the process in the tiny central thermonuclear core this zone should be considered by the cell size $\Delta r =$10$^{-10}$ m in the bubble with radius 10$^{-5}$ m. The same problem exists with the thin boundary layers near the interface.
Three-dimensional analysis for the shape of the bubble supports the assumption of a spherically symmetrical flow to produce the concentration of the energy in the tiny core.
All these effects are crucial for the prediction of the thermonuclear
reaction intensity.
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